Congruent numbers and Heegner points
نویسندگان
چکیده
منابع مشابه
Global Divisibility of Heegner Points and Tamagawa Numbers
We improve Kolyvagin’s upper bound on the order of the p-primary part of the Shafarevich-Tate group of an elliptic curve of rank one over a quadratic imaginary field. In many cases, our bound is precisely the one predicted by the Birch and Swinnerton-Dyer conjectural formula.
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Elliptic curves over Q are equipped with a systematic collection of Heegner points arising from the theory of complex multiplication and defined over abelian extensions of imaginary quadratic fields. These points are the key to the most decisive progress in the last decades on the Birch and Swinnerton-Dyer conjecture: an essentially complete proof for elliptic curves over Q of analytic rank ≤ 1...
متن کاملHeegner points, Heegner cycles, and congruences
We define certain objects associated to a modular elliptic curve E and a discriminant D satisfying suitable conditions. These objects interpolate special values of the complex L-functions associated to E over the quadratic field Q( √ D), in the same way that Bernouilli numbers interpolate special values of Dirichlet L-series. Following an approach of Mazur and Tate [MT], one can make conjecture...
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In this paper we formulate a conjecture which partially generalizes the Gross-Kohnen-Zagier theorem to higher weight modular forms. For f ∈ S2k(N) satisfying certain conditions, we construct a map from the Heegner points of level N to a complex torus, C/Lf , defined by f . We define higher weight analogues of Heegner divisors on C/Lf . We conjecture they all lie on a line, and their positions a...
متن کاملHeegner Points: The Beginnings
Dick Gross and I were invited to talk about Heegner points from a historical point of view, and we agreed that I should talk first, dealing with the period before they became well known. I felt encouraged to indulge in some personal reminiscence of that period, particularly where I can support it by documentary evidence. I was fortunate enough to be working on the arithmetic of elliptic curves ...
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ژورنال
عنوان ژورنال: Cambridge Journal of Mathematics
سال: 2014
ISSN: 2168-0930,2168-0949
DOI: 10.4310/cjm.2014.v2.n1.a4